Geometry: Is it possible for a line intersecting a plane to be perpendicular to exactly one line in the plane?

Question

I have read in my textbook and searched online, but I haven't found what I need to know. Help? :) Thanks!

Answer 1

Yes provided it s NOT perpendicular to (ie a normal to) the plane.

If it is not perpendicular to the plane then it is perpendicular to the line of intersection of that plane and the plane that contains the point of intersection, to which the line is a normal.

If it is a normal to that plane then it is perpendicular to all lines in the plane passing through the point of intersection

Answer 2

Yes if it intersects the plane at an angle that isn't 90 degrees. Even if the line intersects the plane at 0 degrees ( the line is in the plane), there is still only one perpendicular line.

Answer 3

Well, based on your question ("perpendicular to exactly one line") I dont think it is possible.

A line intesecting a plane at a right angle, will be perpendicular to any and every line on that plane. Only if it intersected at 0 degrees (which I doubt we can really call intersecting), which would essentially make it a line on that plane, would it be perpendicular to exactly one line.

Hope this helps.

Answer 4

A line can bypass intersect one, 2, or 3 coordinate planes. that's impossible for it to intersect none. As examples take the line that passes via the element P(a million,2,3). L1(t) = + t L2(t) = + t L3(t) = + t the place parameter t stages over the real numbers L1 intersects one airplane, L2 intersects 2 planes and L3 intersects 3 planes.

Answer 5

yes.
if the line is not perpendicular ot plane, then one line in the plane is perpendicular to the line intersecting.

Answer 6

If the line coming into the plane is perpendicular to that plane, then it would be perpendicular to any line you could draw on that plane.

Answer 7

no, according to one of the math theorems, there are an infinite number of lines in a plane so if a line is perpendicular to a line in a plane, then there are an infinite number of lines it is perpendicular to in that plane.